Point load solutions for an inclined transversely isotropic rock

The solutions of displacements and stresses induced by three-dimensional point loads in a transversely isotropic rock, where the transversely isotropic planes are inclined with respect to the horizontal loading surface, are proposed in this work. The solutions are derived by performing an efficient double Fourier transform to obtain the integral expressions of displacements and stresses; then, the double inverse Fourier transform and residue calculus are utilized to integrate the contours. Utilizing the double Fourier transform in a Cartesian co-ordinate system is a new approach to solve the displacement and stress components resulting from three-dimensional point loads applied on an inclined transversely isotropic rock. The present solutions demonstrate that the displacements and stresses are significantly affected by the following factors: (1) the rotation of the transversely isotropic planes, (2) the type and degree of rock anisotropy, (3) the geometric position, and (4) the types of three-dimensional loading. The yielded solutions are identical with existing ones if the planes of transverse isotropy are parallel to the horizontal loading surface. Therefore, the dip at an angle of inclination should be taken into account when computing the displacements and stresses in a transversely isotropic rock due to applied loads.